Question

The graph below represents which of the following functions?

Answer 1

First of all, you can see that this is a piecewise polynomial, since it is shaped like a parabola before
`x = 2`, and is a line after
`x = 2` So, option C is surely wrong, because it uses
`x = 3` as splitting point.

Moreover, the way the parabola "bounces" on the x axis, avoiding its negative part, tells us that there is an absolute value. This excludes options B and D, and the answer is thus A.

Answer 2

This is a more difficult one to explain. Let's start with the line to the right. It has a slope (m) of
`(-2)/(2)` = -1 and a y-intercept of +3 (continue the line to see where it crosses the y-axis). So, the equation of that line is: y = -x + 3 when x ≥ 2. This can also be written as y = 3 - x when x ≥ 2. The only option that has that equation is A.

Answer: A